87.22.11 problem 11

Internal problem ID [23756]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 4. The Laplace transform. Exercise at page 199
Problem number : 11
Date solved : Thursday, October 02, 2025 at 09:44:55 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-9 y^{\prime }+18 y&=54 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=0 \\ y^{\prime }\left (0\right )&=-3 \\ \end{align*}

✓ Maple. Time used: 0.042 (sec). Leaf size: 18

ode:=diff(diff(y(t),t),t)-9*diff(y(t),t)+18*y(t) = 54; 
ic:=[y(0) = 0, D(y)(0) = -3]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = 2 \,{\mathrm e}^{6 t}+3-5 \,{\mathrm e}^{3 t} \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 21

ode=D[y[t],{t,2}]-9*D[y[t],{t,1}]+18*y[t]==54; 
ic={y[0]==0,Derivative[1][y][0] ==-3}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -5 e^{3 t}+2 e^{6 t}+3 \end{align*}

✓ Sympy. Time used: 0.132 (sec). Leaf size: 17

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(18*y(t) - 9*Derivative(y(t), t) + Derivative(y(t), (t, 2)) - 54,0) 
ics = {y(0): 0, Subs(Derivative(y(t), t), t, 0): -3} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = 2 e^{6 t} - 5 e^{3 t} + 3 \]